Question: Simplify the following expression: $ t = \dfrac{10}{7} - \dfrac{9y}{4y + 6} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4y + 6}{4y + 6}$ $ \dfrac{10}{7} \times \dfrac{4y + 6}{4y + 6} = \dfrac{40y + 60}{28y + 42} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{9y}{4y + 6} \times \dfrac{7}{7} = \dfrac{63y}{28y + 42} $ Therefore $ t = \dfrac{40y + 60}{28y + 42} - \dfrac{63y}{28y + 42} $ Now the expressions have the same denominator we can simply subtract the numerators: $t = \dfrac{40y + 60 - 63y }{28y + 42} $ Distribute the negative sign: $t = \dfrac{40y + 60 - 63y}{28y + 42}$ $t = \dfrac{-23y + 60}{28y + 42}$